Chemical Kinetics - Result Question 20
####20. Mechanism of a hypothetical reaction
[2017] $X_2+Y_2 \to 2 X Y$ is given below :
[2018]
(i) $X_2 \to X+X$ (fast)
(ii) $X+Y_2 \rightarrow X Y+Y$ (slow)
(iii) $X+Y \to X Y$ (fast)
The overall order of the reaction will be :
(a) 2
(b) 0
(c) 1.5
(d) 1
Show Answer
Solution:
- (c) Overall rate $=k[X][Y_2]$
$k=$ rate constant
Assuming step (i) to be reversible, its equilibrium constant,
$k _{\text{eq }}=\frac{[X]^{2}}{[X_2]} \Rightarrow[X]^{2}=k _{\text{eq }}[X_2] ;$
$[X]=k _{e q}^{\frac{1}{2}}[X_2]^{\frac{1}{2}}$
From eq (1) and (2)
Rate $=k _{e q}{ }^{\frac{1}{2}}[X_2]^{\frac{1}{2}}[Y_2]$
Overall order $=\frac{1}{2}+1=\frac{3}{2}=1.5$
The overall reaction rate depends on the rate of the slowest step.
i.e., Overall rate $=$ Rate of slowest step
